A novel importance measure considering multi-constraints for RAP optimization of 1-out-of-n subsystems with mixed redundancy strategy

Intelligent optimization algorithms are the mainstream approach to solving redundancy allocation problems (RAP) with challenging features. Since importance measures (IM) can identify critical components, the combination of IM-based local optimization and intelligent algorithms has wide applications in various optimization problems; however, it is less studied in RAP. Existing IMs also failed to address both the objective function and multiple constraints like cost and weight; this may result in an imprecise identification of critical subsystems for RAP optimization. This paper considers a RAP with a mixed strategy, i.e., active and standby strategies can be applied to a subsystem simultaneously. Two novel IMs are proposed based on a Lagrangian function: cost-centric RAP-based importance (CRI) and weight-centric RAP-based importance (WRI). CRI (WRI) reveals the comprehensive effect of cost (weight) consumption on the system reliability and other resources. A local optimization algorithm guided alternately by CRI and WRI is presented to adjust the redundancy level of subsystems; then, this algorithm is introduced into a genetic algorithm (GA) to determine the component types and redundancy level of all subsystems. Compared with other algorithms and previous studies, the superiority of the proposed hybrid GA is demonstrated via numerical experiments and a well-known benchmark example.